i actually thought the opposite. i found it extremely illuminating to see exp(ix) partition the power series into even and odd terms and collect into cos and sine.
i just always thought of the chain of functions that are their own derivatives.
f = f' => f = exp
f = f'' => f = cosh or sinh
f = f'''' = -f'' => f = cos or sine
if you dont skip cosh/sinh the pattern makes more sense.
i just always thought of the chain of functions that are their own derivatives.
f = f' => f = exp
f = f'' => f = cosh or sinh
f = f'''' = -f'' => f = cos or sine
if you dont skip cosh/sinh the pattern makes more sense.
and obviously f = f'''' strongly suggests 1 = i^4